Holt Algebra 1 10-6 Theoretical Probability 10-6 Theoretical Probability Holt Algebra 1 Warm Up Warm Up Lesson Presentation Lesson Presentation Lesson

Holt Algebra 1

10-6 Theoretical Probability10-6 Theoretical Probability

Holt Algebra 1

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Holt Algebra 1

10-6 Theoretical Probability

Warm UpAn experiment consists of spinning a spinner 8 times. The spinner lands on red 4 times, yellow 3 times, and green once. Find the experimental probability of each event.

1. The spinner lands on red.

2. The spinner does not land on green.

3. The spinner lands on yellow.

Holt Algebra 1


Determine the theoretical probability of an event.Convert between probabilities and odds.

Objectives

Holt Algebra 1


When the outcomes in the sample space of an experiment have the same chance of occurring, the outcomes are said to be equally likely.

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The theoretical probability of an event is the ratio of the number of ways the event can occur to the total number of equally likely outcomes.

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An experiment in which all outcomes are equally likely is said to be fair. You can usually assume that experiments involving coins and number cubes are fair.

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Example 1A: Finding Theoretical Probability

An experiment consists of rolling a number cube. Find the theoretical probability of each outcome.

rolling a 5There is one 5 on a number

cube.

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Example 1B: Finding Theoretical Probability


rolling an odd number

There 3 odd numbers on

a cube.

= 0.5 = 50%

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Example 1C: Finding Theoretical Probability


rolling a number less than 3

There are 2 numbers

less three.

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The probability of an event can be written as P(event). P(heads) means “the probability that heads will be the outcome.”

Reading Math

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When you toss a coin, there are two possible outcomes, heads or tails. The table below shows the theoretical probabilities and experimental results of tossing a coin 10 times.

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The sum of the probability of heads and the probability of tails is 1, or 100%. This is because it is certain that one of the two outcomes will always occur.

P(event happening) + P(event not happening) = 1

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The complement of an event is all the outcomes in the sample space that are not included in the event. The sum of the probabilities of an event and its complement is 1, or 100%, because the event will either happen or not happen.

P(event) + P(complement of event) = 1

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Example 2: Finding Probability by Using the Complement

A box contains only red, black, and white blocks.

The probability of choosing a red block is , the

probability of choosing a black block is . What

is the probability of choosing a white block?

P(red) + P(black) + P(white) = 100%

75% + P(white) = 100%

25% + 50% + P(white) = 100%

–75% –75%

P(white) = 25%

Either it will be a white block or not.

Subtract 75% from both sides.

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Odds are another way to express the likelihood of an event. The odds in favor of an event describe the likelihood that the event will occur. The odds against an event describe the likelihood that the event will not occur.

Odds are usually written with a colon in the form a:b, but can also be written as a to b or .

Holt Algebra 1


Holt Algebra 1


The two numbers given as the odds will add up to the total number of possible outcomes. You can use this relationship to convert between odds and probabilities.

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You may see an outcome called “favorable.” This does not mean that the outcome is good or bad. A favorable outcome is the outcome you are looking for in a probability experiment.

Reading Math

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Example 3A: Converting Between Odds and Probabilities

The probability of rolling a 2 on a number

cube is . What are the odds of rolling a 2 ?

Odds in favor are 1:5.

The probability of rolling a 2 is . There are 5 unfavorable

outcomes and 1 favorable outcome, thus the odds are 1:5.

Holt Algebra 1


Example 3B: Converting Between Odds and Probabilities

The odds in favor of winning a contest are 1:9. What is the probability of winning the contest?

The odds in favor of winning are 1:9, so the odds against are 9:1. This means there is 1 favorable outcome and 9 unfavorable outcomes for a total of 10 possible outcomes.

The probability of winning the contest is

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Example 3C: Converting Between Odds and Probabilities

The odds against a spinner landing on red are 2:3. What is the probability of the spinner landing on red?

The odds against landing on red are 2:3, so the odds in favor are 3:2. This means there are 3 favorable outcomes and 2 unfavorable outcomes for a total of 5 possible outcomes.

The probability of landing on red is

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Holt Algebra 1 10-6 Theoretical Probability 10-6 Theoretical Probability Holt Algebra 1 Warm Up Warm Up Lesson Presentation Lesson Presentation Lesson